Related papers: Bayesian inverse problems with partial observation…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated…
We consider the problem of assessing goodness of fit of a single Bayesian model to the observed data in the inverse problem context. A novel procedure of goodness of fit test is proposed, based on construction of reference distributions…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (modes) for posterior distributions arising from model-specific…
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem…
Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…
Posterior contractions rates (PCRs) strengthen the notion of Bayesian consistency, quantifying the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of the true model, with probability tending to 1 or…
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…